Question

A small town has two local high schools. High School A currently has 800 students

and is projected to grow by 35 students each year. High School B currently has 550
students and is projected to grow by 85 students each year. Let A represent the
number of students in High School A in t years, and let B represent the number of
students in High School B after t years. Write an equation for each situation, in terms
of t, and determine the interval of years, t, for which High School A will have more
students than High School B.

Answer 1

T < 5

Explanation:

High School A: A(t) = 800 + 35t

High School B: B(t) = 550 + 85t

To find the interval of years in which High School A will have more students than High School B, we need to find the years in which A(t) > B(t).

So, we need to solve the inequality A(t) > B(t)

800 + 35t > 550 + 85t

250 > 50t

t < 5

Therefore, High School A will have more students than High School B for the first five years.

The interval of years, t, for which High School A will have more students than High School B is t < 5